Question

How do you differentiate `(2x^2-4x+4)e^x`?

Answer 1

for a product of functions you have the formula
`if f(x)=g(x)*h(x)`
`if f'(x)=g'(x)*h(x)+g(x)*h'(x)`

so lets start :)
your functions are `g(x)=2x^2-4x+4` and `h(x)=e^x`

so `f'(x)=(4x-4)*e^x+(2x^2-4x+4)*e^x=(4x-4+2x^2-4x+4)*e^x=2x^2e^x`

remember that `d/dxe^u=e^u*d/dxu` in this case as u=x; du/dx=1